613.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 613

Reference: erdosproblems.com/613

Imports (1)

FormalConjecturesUtil

theorem Erdos613.erdos_613 Erdős Problem 613: Let $n \geq 3$ and $G$ be a graph with $\binom{2n+1}{2} - \binom{n}{2} - 1$ edges sorry line 36 source
Source documentation
Erdős Problem 613: Let $n \geq 3$ and $G$ be a graph with $\binom{2n+1}{2} - \binom{n}{2} - 1$ edges. Must $G$ be the union of a bipartite graph and a graph with maximum degree less than $n$?

depends on sorry what this means
Statement uses: Iff, False, Nat, GE.ge, OfNat.ofNat, Fintype, SimpleGraph, DecidableRel, SimpleGraph.Adj, Eq, Finset.card, Sym2, SimpleGraph.edgeFinset, HSub.hSub, Nat.choose, HAdd.hAdd, HMul.hMul, Exists, And, Max.max and 6 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
30 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_613 :
    answer(False) ↔
      ∀ n ≥ 3, ∀ (V : Type*) [Fintype V] (G : SimpleGraph V), [DecidableRel G.Adj] →
        G.edgeFinset.card = Nat.choose (2 * n + 1) 2 - Nat.choose n 2 - 1 →
        ∃ (B D : SimpleGraph V), [DecidableRel B.Adj] → [DecidableRel D.Adj] →
          G = B ⊔ D ∧ B.IsBipartite ∧ ∀ v, D.degree v < n := by
…
```